LAUSR

This paper develops rigorous lower-bound shakedown solutions for pavement structures subjected to Hertz loads both in plane strain and three-dimensional (3D) models. Firstly, a necessary shakedown condition is derived based on Melan’s shakedown theorem and the use of Prandtl–Reuss theory in conjunction with von Mises criterion, which gives a maximum value to the rigorous shakedown limit. Secondly, the rigorous lower-bound shakedown solution is established uses a self-equilibrated critical residual stress field with an optimisation procedure. As expected, the necessary shakedown condition gives larger values of normalised shakedown limits than that of the normalised rigorous lower-bound shakedown solution, with the maximum difference of 93%. Also observed is that the 3D model always overestimates the normalised rigorous shakedown limits of the plane strain model by approximately 8–13%, while the two models capture approximately the same trend of normalised rigorous shakedown limits varied with frictional coefficient. Finally, the parametric studies on normalised rigorous shakedown limit of pavements in terms of frictional coefficient and Poisson’s ratio are performed. It shows that the normalised rigorous shakedown limits are proportional to material yield stress but decrease markedly with raising frictional coefficient; while the effect of the Poisson’s ratio on normalised rigorous shakedown limits is marginally. In addition, the critical residual stress fields lie between two residual stress limits, which intersect beneath the surface for small μ, while tend to converge at the half-space surface when μ = 0.3, indicating that the failure mode of the pavement changes from subsurface failure to surface failure when increasing the frictional coefficient μ. As a result, the present shakedown solutions can provide reference to the design of pavements subjected to rolling and sliding loading contact.